Solve your IGNOU Doubts

Question:

A single observation was taken from a population with p.d.f. $f(x,\theta)=\frac{2}{\theta^2}(\theta-x),$ $0\leq x\leq\theta.$

Obtain $100(1-\alpha )%$ confidence interval for θ.

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Question:

Which of the following statements are true and which are false? Give reasons for your answer.

a) In an LP model, the feasible solution space can be effected when redundant constraints are deleted.

b) If the primal LPP has an optimal solution, then the set of feasible solution to its dual is bounded.

c) In a simplex iteration, an artificial variable can be dropped all together from the simplex table once the variable becomes non basic.

d) The addition of a constant to all the elements of a payoff matrix in a two – person zero sum game can affect only the value of the game, not the optimal mix of the strategies.

e) There may be a balanced transportation problem without any feasible solution.

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Question:

A group of 250 items with mean 15.6 and standard deviation $\sqrt{13.44}$ . has been divided into two groups. The first has 100 items with mean 15 and standard deviation 3. Find the standard deviation of the second group.

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Question:

X , X and X3 is a random sample of size 3 from a population with mean µ and variance $\sigma ^2.$ $T_1,T_2$ . and $T_3$ are the estimators to estimate µ, and are given by ; $T1=X_1+X_2-X_3;T_2=2X_1+3X_2-4X_2$ and $T_3(\lambda X_1+X_2+X_3).$

i) Are T1 and T2 unbiased? Give reason.
ii) Find the value of λ such that T3 is unbiased.
iii) Which is the best estimator? State giving reasons.

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Question:

Draw the cumulative frequency curves for the following distribution:

Marks	No. of Students
0 – 10	4
10 – 20	8
20 – 30	11
30 – 40	15
40 – 50	12
50 – 60	6
60 – 70	3

From the graph, obtain the median.

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Question:

The probability that a student passes a Physics test is $\frac{2}{3}$
and the probability that the student passes both a Physics test and an English test is $\frac{14}{15}$ The probability that the
student passes at least one test is $\frac{4}{5}$ What is the probability that the student passes the English test?

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Question:

b) i) Calculate the third-degree Taylor polynomial abou $x_0=0$ for $f(x)=(1+x)^{1/2}$

ii) Use the polynomial in part (i) to approximate $\sqrt{1.1}$ and find a bound for the error involved.

iii) Use the polynomial in part (i) to approximate $\int _{0}^{0.1}(1+x)^{1/2}dx.$

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Question:

$\frac{}{}$ $\sqrt{\frac{1+x^4}{x^4}}$

1.414

1.031

1007

1.002

1.001

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Question:

Let X be a single observation from the p.d.f. $f(x,\theta )=\theta e^{\theta x},0\leq x<\infty .$

If X ≥1 is the critical region for testing $H_0:\theta=2$ against the alternative hypothesis $H_1:\theta=1,$ obtain the values of type I and type II errors.

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Question:

a) Using the following table of values, find approximately by Simpson’s rule, the arc ength of the graph $y=\frac{1}{x}$ between the points (1, 1) and $\left ( 5,\frac{1}{5} \right )$

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Question:

c) Show that $u_x=c_1e^a^x+c^2e^{-ax}$ is a solution of the difference equation $u_x+1-2u_xcosh\,a+u_{x-1}=0.$

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Question:

a) Find the mean and standard deviation for the following data:

Class interval	Frequency
0 – 10	5
10 – 20	10
20 – 30	14
30 – 40	15
40 – 50	6

b) State Chebychev’s inequality. Hence obtain the lower bound for $P[-1<x<9]$ if the E(x) and $E(x^2)$ of x are 4 and 20 respectively.

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Question:

b) Use modified Euler’s method to find the approximate solution of IVP

$y'=2xy,y(1)=1$ at $x=1.5$ with $h=0.1$

If the exact solution is $y(x)=e^{x^{2-1}},$ find the error.

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Question:

The police plans to enforce speed limits by using radar traps of 4 different locations within the city. The radar traps at each of the locations $L_1,L_2,L_3$ and $L_4$ are operated 40 % 30% 20% and 30%, of time. If a person who is speeding on h, is way to work has probabilities of 0.2, 0.1, 0.5 and 0.2 respectively of passing through these locations. What is the probability that the person will receive a speeding challan.

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Question:

a) Compute the values of

$1=\int _{0}^2{}\frac{dx}{1+x^2}$

by using the trapezoidal rule with $h=0,50.25,0,125.$ Improve this value by using the Romberg’s method. Compare your result with the true value.

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Question:

The following information about advertising expenditures and sales of a company is given below:

	Advertising expenditure (x) Lakhs ( )	Sales (y) Lakhs ()
Average	10	90
Variance	9	144
Correlation Coefficient between x and y is 0.8.

What should be the advertising budget if the company wants to attain sales target of Image ignouassignments-ignouacademy-com--p-solve-76382 120 Lakhs?

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Question:

c) Using the classical R-K method of $0(h^4)$ calculate approximate solution of the IVP, $y'=1-x+4y,y(0)=1$ at $x=0.6,$ taking $h=0.1$ and $0.2.$ Use extrapolation technique to improve the accuracy.

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Question:

b) A table of values is to be constructed for the function $f(x)$ given by $=\frac{1}{1+x}$ in the interval [1, 4] with equal step length. Determine the spacing h such that quadratic interpolation gives result with accuracy $1\times 10^{-6}.$

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Question:

a) Show that $\sqrt{1+\mu ^2\delta ^2}=1+\frac{\delta ^2}{2}$ where $\mu$ and $\delta$ are the average and central differences operators, respectively.